The Florida Court of Appeals for the Third District, the NRA, the Florida Legislature, the Florida Carry legal dept. and I will reconsider...
Nope, still a problem.
You are conflating two distinct but related issues.
Yes, you can legally have a firearm in your glovebox under current law.
An operator of a parking lot can prohibit you from parking in their lot and trespass you from the property just because you have a legally possessed firearm stored in your car legally under current law.
SB 234 fixes that for licensees.
Please read the exact language of this part of the bill:
"(b) A person licensed under this section shall not be prohibited from carrying or storing a firearm in a vehicle for lawful purposes."
this is MUCH stronger than the current law:
"790.25(5) POSSESSION IN PRIVATE CONVEYANCE.—Notwithstanding subsection (2), it is lawful and is not a violation of s. 790.01 for a person 18 years of age or older to possess a concealed firearm or other weapon for self-defense or other lawful purpose within the interior of a private conveyance, without a license, if the firearm or other weapon is securely encased or is otherwise not readily accessible for immediate use. Nothing herein contained prohibits the carrying of a legal firearm other than a handgun anywhere in a private conveyance when such firearm is being carried for a lawful use. Nothing herein contained shall be construed to authorize the carrying of a concealed firearm or other weapon on the person. This subsection shall be liberally construed in favor of the lawful use, ownership, and possession of firearms and other weapons, including lawful self-defense as provided in s. 776.012."